Holographic optic elements, commonly referred to as HOEs, can be used as a substitute for, or a supplement to, convention refractive optical elements. One of the common problems associated with the use of HOEs is aberration, particularly when the HOE is provided with a low f/#. To resolve the aberration problem, a number of researchers have developed computer generated holograms having a simulated interference pattern recorded thereon which was generated using a computer model which sought to minimize aberration. Examples of computer generated holograms are discussed in Latta, J. N., "Computer-Based Analysis of Hologram Imagery and Aberration, I. Hologram Types and Their Non-chromatic Aberrations", Applied Optics, Vol. 10, No. 3, Page 599, March 1971; Latta, J. N., "Computer-Based Analysis of Hologram Imagery and Aberrations, II. Aberrations Induced by a Wavelength Shift", Applied Optics, Vol. 10, No. 3, Page 609, March 1971; Fairchild, R. C.,; Fienup, J. R., "Computer-Originated Aspheric Holographic Optical Elements", Optical Engineering, Vol. 21, No. 1, Page 133, January/February 1982; and Winick, K. A.; Fienup, J. R., "Optimum Holographic Elements Recorded With Nonspherical Wave Fronts", Journal of the Optical Society of America, Vol. 73, No. 2, Page 208, February 1983, which are incorporated by reference herein.
Since HOEs are recorded using photographic film, the wavelength of recording is limited by the range of wavelengths in which the film can be used and still have reasonable resolution. Available photographic film has such poor resolution in the infrared (IR) and near infrared (near IR) range that HOEs to be used in these ranges are preferably fabricated in the visible range where photographic film resolution is superior. There are severe aberration problems caused by recording a HOE at one wavelength and using it in another. By appropriately selecting a recording geometry, one or more of the various aberrations may be reduced or eliminated typically, however, not without a tradeoff in the terms of some other form of aberration. The effects recording geometry and wavelengths on the various types of aberration, i.e., spherical aberration, coma, astigmatism, curvature of field and distortion, have been documented in the literature as best shown in Meier, Reinhard W., "Magnification and Third-Order Aberrations in Holography", Journal of the Optical Society of America, Vol. 55, No. 8, Page 987, August 1965; Upatnieks, J.; Vander Lugt, A.; Leith, E., "Correction of Lens Aberrations by Means of Holograms", Applied Optics, Vol. 5, No. 4, Page 589, April 1966; and Champagne, Edwin B., "Nonparaxial Imaging, Magnification, and Aberration Properties in Holography", Journal of the Optical Society of America, Vol. 57, No. 1, Page 51, January 1967, which are incorporated by reference herein. Once one understands the causes of aberration using modern computer modeling techniques, a hologram recording geometry may be selected in which a HOE can be recorded in visible light and used in the IR or near IR range. The resulting HOEs made using normal construction techniques, however, are not diffraction limited at low f#s due to the influence of higher order phase error. In order to fabricate diffraction limited low f/# proposed to be used in the IR range, it was previously believed that computer generated hologram methods were necessary.